ThmDex – An index of mathematical definitions, results, and conjectures.

ThmDex – An index of mathematical definitions, results, and conjectures.

Result R5251 on D3838: Gamma random positive real number

Exponential random positive real number is a gamma random positive real number

Formulation 0

Let $T \in \text{Exponential}(\theta)$ be an D214: Exponential random positive real number.

Then \begin{equation} T \overset{d}{=} \text{Gamma}(1, \theta) \end{equation}

Proofs

Proof 0

Let $T \in \text{Exponential}(\theta)$ be an D214: Exponential random positive real number.

This result is a particular case of R5243: Finite sum of uncorrelated identically distributed exponential random positive real numbers is a gamma random random positive real number. $\square$